Find the Indicated Roots $7 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

question 306

Multiple Choice

Find the indicated roots. Write the answer in polar form.
-Fifth roots of $7 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

• A) \(\sqrt [ 5 ] { 7 } \left( \cos \frac { \pi } { 15 } + \mathrm { i } \sin \frac { \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 7 \pi } { 15 } + \mathrm { i } \sin \frac { 7 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 13 \pi } { 15 } + \mathrm { i } \sin \frac { 13 \pi } { 15 } \right)\), \(\sqrt [ 5 ] { 7 } \left( \cos \frac { 19 \pi } { 15 } + i \sin \frac { 19 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)\)
• B) \(\frac { 7 } { 5 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\), \(\frac { 7 } { 5 } \left( \cos \frac { 19 \pi } { 15 } + i \sin \frac { 19 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)\)
• C) \(\frac { 7 } { 5 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 4 \pi } { 15 } + i \sin \frac { 4 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right)\), \(\frac { 7 } { 5 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\)
• D) \(\sqrt [ 5 ] { 7 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 4 \pi } { 15 } + i \sin \frac { 4 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right)\), \(\sqrt [ 5 ] { 7 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\)

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Pirates who operated from North Africa, based primarily in the ports of Algiers, Tunis, and Tripoli, known for capturing and enslaving European merchants and travelers in the Mediterranean from the 16th to the 19th centuries.

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A journey undertaken by Meriwether Lewis and William Clark from 1804 to 1806, across North America to explore the lands west of the Mississippi River acquired in the Louisiana Purchase.

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